Problem: What do the following two equations represent? $-2x+3y = 2$ $-2x-4y = 5$
Solution: Putting the first equation in $y = mx + b$ form gives: $-2x+3y = 2$ $3y = 2x+2$ $y = \dfrac{2}{3}x + \dfrac{2}{3}$ Putting the second equation in $y = mx + b$ form gives: $-2x-4y = 5$ $-4y = 2x+5$ $y = -\dfrac{1}{2}x - \dfrac{5}{4}$ The slopes are not the same, so the lines are not equal or parallel. The slopes are not negative inverses of each other, so the lines are not perpendicular. The correct answer is none of the above.